🌊Wave Speed
The Wave Speed Equation
The speed of a wave is related to its frequency and wavelength:
v = fλ
This fundamental wave equation connects three key quantities. Note: the speed is determined by the MEDIUM, not by the frequency or amplitude.
For example, the speed of sound in air (≈ 343 m/s at 20°C) is fixed by air properties. A higher-frequency sound wave will simply have a shorter wavelength.
For a transverse wave on a string: v = √(F_T/μ) where F_T = tension and μ = mass per unit length.
Think About It
If you increase the tension in a guitar string, the pitch (frequency) goes up. From v = fλ, does the wavelength change? What determines the wavelength?
✏️ Worked Example
Problem: A sound wave in air has a frequency of 440 Hz (middle A). What is its wavelength? (v_sound = 340 m/s)
📐 Key Equations
Wave speed
v = fλv_string = √((F_T)/(μ))v_sound ≈ 343 m/s at 20°C⚠️ Common Mistakes
Misconception: Increasing the frequency of a wave in a fixed medium also increases its speed.
✓ Correct thinking: Wave speed is determined by the medium, not the frequency. Increasing frequency shortens the wavelength to keep v = fλ constant.
Why: Think of sound in air: a high-pitched voice and a low-pitched voice both travel at 343 m/s. The difference is wavelength, not speed.
Misconception: A louder sound travels faster than a quieter sound.
✓ Correct thinking: Amplitude (loudness) has no effect on wave speed. All sounds in the same medium travel at the same speed.
Why: Speed depends on medium properties (density, elasticity), not on how much energy the wave carries.
Misconception: Wave speed and the speed of individual medium particles are the same thing.
✓ Correct thinking: Wave speed is how fast the disturbance propagates. Particle speed is how fast molecules oscillate back and forth — a separate quantity.
Why: A slow-moving wave can have very fast-moving particles if the amplitude is large, and vice versa.
📝 Practice Problems
Try these problems. Check your answer when ready.
A sound wave has frequency 680 Hz and speed 340 m/s. What is its wavelength?
λ = v/fA wave travels at 300 m/s and has a wavelength of 0.75 m. What is its frequency and period?
A guitar string has tension 80 N and linear mass density 0.005 kg/m. What is the wave speed in the string?
v = √(F_T/μ)The tension in a string is quadrupled while the linear density stays the same. By what factor does the wave speed change?
In medium A, a 500 Hz wave has wavelength 0.4 m. In medium B, the same wave has wavelength 1.2 m. What are the wave speeds in each medium? Which medium is "faster"?
A wave in a string has v = 200 m/s, f = 100 Hz, and amplitude 0.02 m. If you double the tension (keeping μ constant) and double the frequency, what is the new wavelength?
v_new = √(2) · v_old, λ = v/fFinished reading through this lesson?